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" Let AB and C be two unequal magnitudes, of which AB is the greater. If from AB there be taken more than its half, and from the remainder more than its half, and so on ; there shall at length remain a magnitude less than C. For C may be multiplied, so... "
The Elements of Euclid for the Use of Schools and Colleges: Comprising the ... - Side 244
av Euclid, Isaac Todhunter - 1883 - 400 sider
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845
...EFGH above the space S; because, by the preceding Lemma, if from the greater of two unequal magnitudes there be taken more than its half, and from the remainder...there shall at length remain a magnitude less than the least of the proposed magnitudes. Let then the segments EK, KF, FL, LG, GM, MH, HN, NE be those...
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A system of practical mathematics; being no.xvi. of a new series of school-books

Scottish school-book assoc - 1845
...given line. For it has been shown in the proposition that this is equivalent to taking away from EC more than its half, and from the remainder more than its half, and so on continually ; .-. (Prop. 73, Cor.) the quantity ultimately left is less than any given quantity. PROPOSITION...
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The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846
...less than any other given magnitude less than the former. Let AB and C be the two given magnitudes, of which AB is the greater : if from AB there be taken a magnitude greater than its half, and from the remainder a magnitude greater than its half, and so...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1846 - 317 sider
...a magnitude less than the least of the proposed magnitudes. Let AB and C be two unequal magnitudes, of which AB is the greater. If from AB there be taken away its half, and from the remainder its half, and so on ; there shall at length remain a magnitude...
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The definitions, postulates, axioms, and enunciations of the propositions of ...

Euclides - 1848
...equal to one another. BOOK XII. PROPOSITIONS. LEMMA I. IP from the greater of two unequal magnitudes, there be taken more than its half, and from the remainder...there shall at length remain a magnitude less than the least of the proposed magnitudes. (Book x. Prop, i.) PROP. I. THEOREM. Similar polygons inscribed...
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1855
...of the proposed magnitudes. Let AB and C be two unequal magnitudes, of the same kind, of which \ B is the greater. If from AB there be taken more than...the remainder more than its half, and so on ; there will at length remain a magnitude less than C. For C may be multiplied so as at length to become greater...
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The Elements of Euclid, with many additional propositions, and explanatory ...

Euclides - 1855
...hexagon. T. Of the Multiples of Magnitudes. HYPOTHESES. If from the greater of two unequal magnitudes, there be taken more than its half, and from the remainder more than its half, and so on. If one magnitude be the same multiple of another, which a part taken from the first is of a part taken...
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The Elements of Euclid with Many Additional Propositions and Explanatory Notes

Eucleides - 1860
...160). V. 6. . . V. 1. . . V. c. (p. 34). HYPOTHESES. If from the greater of two unequal magnitudes, there be taken more than its half, and from the remainder more than its half, and so on. If one magnitude be the same multiple of another, which a part taken from the first is of a part taken...
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Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ...

Euclides - 1860
...a magnitude less than the least of the proposed magnitudes. Let AB and C be two unequal magnitudes, of which AB is the greater. If from AB there be taken away its half, and from the remainder its half, and so on, there shall at length remain a magnitude...
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The school edition. Euclid's Elements of geometry, the first six books, by R ...

Euclides - 1864
...EFGH above the space 8; because, by the preceding Lemma, if from the greater of two unequal magnitudes there be taken more than its half, and from the remainder...there shall at length remain a magnitude less than the least of the proposed magnitudes. Let then the segments EK, KF, FL, LG, GM, MH, HN, NE be those...
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